Try it yourself! Find the slope (m) between the two points (3, 4) and (-8, 5). m = -11
Try it yourself! Find the slope using the graph below. (2,4) (-4,-2) m = 1
Finding y-intercept By definition, “In coordinate geometry, the y-intercept is the y-value of the point where the graph of a function or relation intercepts the y-axis of the coordinate system.” Definition found at en.wikipedia.org/wiki/Y-intercept
Try it yourself! Use the graph to find the y-intercept. b = (0,1) x-coordinate will always be zero
Try it yourself! Write the point-slope equation for the line with slope of -½ and y-intercept of 5. m = -½ b = 5 y = -½x + 5 Plug into equation
Try it yourself! Given the points (1,2) and (4,3), and y-intercept of 5/3, write the point-slope equation of the line. 2.) Plug the slope into the equation next with the given y-intercept. 1.) Find the slope using the two given points.
Write the point-slope equation using the graph below. Try it yourself! 1.) Find the y-intercept. b = (0,-2) 2.) Find the slope by starting at the y-intercept, and counting up and over until you hit another point on the line. (rise over run) We can count up 1, and left 1, and hit another point on the line, so the slope = 1/1. Plug into equation. 2 1 -1 -2 y = 1x - 2
What do two parallel lines have in common? Two parallel lines share the same slope, but pass through a different set of points
Let’s look at some graphs of parallel lines… Slope of line 1: 0 Slope of line 2: 0 Slope of line 1: undefined Slope of line 2: undefined
Writing point-slope equations using parallel lines Write the point-slope equations for each line given the points below. Line 1: (2,3) and (4,6), b = 0 Line 2: (5,6) and (7,9), b = -3/2 y = 3/2x + 0 y = 3/2x -3/2
Using an equation to write another that is parallel to it… Given y = 4x + 1, write the equation of its parallel line that passes through the point (1,3). Since the slopes are the same, we will start by writing y = 4x + b. Next, solve for b by plugging in the point given. x = 1, and y = 3, so 3 = 4(1) + b. Solving for b, we get b = -1. To finish the problem, we will plug b into our original equation shown in blue. y = 4x - 1
Try it yourself! Use the graph to find the equation of the line parallel to it that passes through (-3, -6). Then graph it. First, find the slope of the given line using rise over run. m = (-4/2) Plug into y = mx + b and solve for b by using the point given. x = -3, y = -6 -6 = (-4/2)(-6) + b b = -12 4 2 y = (-4/2)x - 12
Exit Questions What is the y-intercept? What is the point-slope equation in general? Find the slope between points (-1,1) and (3,-4). What do parallel lines have in common?